Proceedings of the Edinburgh Mathematical Society. Series II (Proc. Edinb. Math. Soc. (2)) (20230101), 66, no.~3, 689-709. ISSN: 0013-0915 (print).eISSN: 1464-3839.
Subject
19 $K$-theory -- 19A Grothendieck groups and $K_0$ 19A22 Frobenius induction, Burnside and representation rings
20 Group theory and generalizations -- 20C Representation theory of groups [See also 19A22 20C05 Group rings of finite groups and their modules 20C20 Modular representations and characters 20C33 Representations of finite groups of Lie type
This article is a continuation of Part I [J. Algebra {\bf 598} (2022), 308--350; MR4379284] by B. Böhmler and the authors. In Part I, the trivial source character tables in characteristic $\ell$ were computed for the special linear group ${\rm SL}_2(q)$ over the finite field $\Bbb{F}_q$, where $\ell$ and $q$ are odd and $\ell\nmid q$. In the present article, the trivial source character tables are computed for $G={\rm SL}_2(2^f)={\rm PSL}_2(2^f)$, over the finite field $\Bbb{F}_{2^f}$, in odd characteristic $\ell$ dividing $|G|$, that is, $\ell\mid 2^f-1$ or $\ell\mid 2^f+1$.